Conversion to HEALPix map

To achieve the conversion into spherical harmonics it is necessary to project the beam into a HELAPix map, this allows grasp2alm to use built-in functions such as the spherical harmonics transform.

HELAPix map produces a subdivision of a spherical surface in which each pixel covers the same surface area as every other pixel. The resolution is controlled by the parameter \(N_{\mathrm{side}}\) related to the number of pixels by the simple equation \(N_{\mathrm{pixel}}=12N_{\mathrm{side}}^2\).

The discretization performed by Grasp is different from the one used in a HEALPix map, to avoid gaps in the map it is necessary to make an interpolation of the beam at a given direction.

The interpolation is performed using scipy.interpolate.RegularGridInterpolator; starting from the regular grid \(\theta, \phi\) (or \(u,v\)) returned by the reading and rotating step, the map is created interpolating the values returned by using healpy.pix2ang.

The interpolation could be performed by choosing between the following methods: linear, nearest, slinear, cubic, quintic and pchip. Moreover, it is possible to choose the value of the pixels that are over the \(\theta, \phi\) boundaries, default is healpy.pixelfunc.UNSEEN.